Properties

Label 416.2.bi.a.307.19
Level $416$
Weight $2$
Character 416.307
Analytic conductor $3.322$
Analytic rank $0$
Dimension $216$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [416,2,Mod(99,416)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(416, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("416.99");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 416 = 2^{5} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 416.bi (of order \(8\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.32177672409\)
Analytic rank: \(0\)
Dimension: \(216\)
Relative dimension: \(54\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 307.19
Character \(\chi\) \(=\) 416.307
Dual form 416.2.bi.a.187.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.672951 - 1.24384i) q^{2} +(1.34047 + 0.555241i) q^{3} +(-1.09427 + 1.67409i) q^{4} +(3.73491 + 1.54705i) q^{5} +(-0.211441 - 2.04098i) q^{6} -0.167444 q^{7} +(2.81869 + 0.234521i) q^{8} +(-0.632754 - 0.632754i) q^{9} +(-0.589131 - 5.68672i) q^{10} +(0.0478422 - 0.115501i) q^{11} +(-2.39636 + 1.63648i) q^{12} +(-1.91671 + 3.05389i) q^{13} +(0.112681 + 0.208273i) q^{14} +(4.14755 + 4.14755i) q^{15} +(-1.60513 - 3.66382i) q^{16} +4.75422 q^{17} +(-0.361232 + 1.21286i) q^{18} +(-2.62674 + 1.08803i) q^{19} +(-6.67692 + 4.55967i) q^{20} +(-0.224453 - 0.0929715i) q^{21} +(-0.175861 + 0.0182187i) q^{22} +(0.822050 + 0.822050i) q^{23} +(3.64815 + 1.87942i) q^{24} +(8.02068 + 8.02068i) q^{25} +(5.08840 + 0.328959i) q^{26} +(-2.16258 - 5.22093i) q^{27} +(0.183229 - 0.280315i) q^{28} +(-0.362881 + 0.876073i) q^{29} +(2.36779 - 7.94999i) q^{30} +(-1.60097 + 1.60097i) q^{31} +(-3.47702 + 4.46210i) q^{32} +(0.128262 - 0.128262i) q^{33} +(-3.19936 - 5.91349i) q^{34} +(-0.625388 - 0.259044i) q^{35} +(1.75169 - 0.366879i) q^{36} +(4.11822 - 9.94226i) q^{37} +(3.12101 + 2.53505i) q^{38} +(-4.26493 + 3.02941i) q^{39} +(10.1647 + 5.23657i) q^{40} +1.57976i q^{41} +(0.0354044 + 0.341749i) q^{42} +(-2.99613 - 7.23329i) q^{43} +(0.141007 + 0.206482i) q^{44} +(-1.38438 - 3.34218i) q^{45} +(0.469298 - 1.57570i) q^{46} +(5.14120 - 5.14120i) q^{47} +(-0.117333 - 5.80247i) q^{48} -6.97196 q^{49} +(4.57891 - 15.3740i) q^{50} +(6.37289 + 2.63974i) q^{51} +(-3.01507 - 6.55052i) q^{52} +(0.952080 + 2.29853i) q^{53} +(-5.03868 + 6.20333i) q^{54} +(0.357373 - 0.357373i) q^{55} +(-0.471971 - 0.0392691i) q^{56} -4.12519 q^{57} +(1.33390 - 0.138188i) q^{58} +(-11.6115 - 4.80965i) q^{59} +(-11.4819 + 2.40481i) q^{60} +(-1.39878 + 3.37697i) q^{61} +(3.06872 + 0.913973i) q^{62} +(0.105951 + 0.105951i) q^{63} +(7.89000 + 1.32208i) q^{64} +(-11.8833 + 8.44076i) q^{65} +(-0.245852 - 0.0732233i) q^{66} +(2.18529 + 5.27576i) q^{67} +(-5.20242 + 7.95898i) q^{68} +(0.645497 + 1.55837i) q^{69} +(0.0986463 + 0.952206i) q^{70} -12.4430i q^{71} +(-1.63514 - 1.93193i) q^{72} +8.93301 q^{73} +(-15.1379 + 1.56825i) q^{74} +(6.29807 + 15.2049i) q^{75} +(1.05291 - 5.58800i) q^{76} +(-0.00801088 + 0.0193400i) q^{77} +(6.63819 + 3.26625i) q^{78} +14.3833 q^{79} +(-0.326920 - 16.1673i) q^{80} -5.51470i q^{81} +(1.96497 - 1.06310i) q^{82} +(-10.2392 + 4.24121i) q^{83} +(0.401255 - 0.274018i) q^{84} +(17.7566 + 7.35503i) q^{85} +(-6.98080 + 8.59435i) q^{86} +(-0.972863 + 0.972863i) q^{87} +(0.161940 - 0.314342i) q^{88} -6.33972i q^{89} +(-3.22552 + 3.97107i) q^{90} +(0.320941 - 0.511354i) q^{91} +(-2.27573 + 0.476636i) q^{92} +(-3.03497 + 1.25713i) q^{93} +(-9.85461 - 2.93505i) q^{94} -11.4939 q^{95} +(-7.13838 + 4.05072i) q^{96} +(-7.29863 - 7.29863i) q^{97} +(4.69179 + 8.67200i) q^{98} +(-0.103356 + 0.0428116i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 4 q^{8} - 8 q^{9} - 4 q^{11} + 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} - 4 q^{19} - 20 q^{20} - 16 q^{21} - 24 q^{22}+ \cdots - 116 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/416\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(287\) \(353\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.672951 1.24384i −0.475848 0.879527i
\(3\) 1.34047 + 0.555241i 0.773920 + 0.320568i 0.734459 0.678653i \(-0.237436\pi\)
0.0394612 + 0.999221i \(0.487436\pi\)
\(4\) −1.09427 + 1.67409i −0.547137 + 0.837043i
\(5\) 3.73491 + 1.54705i 1.67030 + 0.691863i 0.998792 0.0491308i \(-0.0156451\pi\)
0.671512 + 0.740994i \(0.265645\pi\)
\(6\) −0.211441 2.04098i −0.0863202 0.833226i
\(7\) −0.167444 −0.0632878 −0.0316439 0.999499i \(-0.510074\pi\)
−0.0316439 + 0.999499i \(0.510074\pi\)
\(8\) 2.81869 + 0.234521i 0.996557 + 0.0829157i
\(9\) −0.632754 0.632754i −0.210918 0.210918i
\(10\) −0.589131 5.68672i −0.186300 1.79830i
\(11\) 0.0478422 0.115501i 0.0144250 0.0348250i −0.916503 0.400028i \(-0.869000\pi\)
0.930928 + 0.365203i \(0.119000\pi\)
\(12\) −2.39636 + 1.63648i −0.691770 + 0.472410i
\(13\) −1.91671 + 3.05389i −0.531599 + 0.846996i
\(14\) 0.112681 + 0.208273i 0.0301154 + 0.0556633i
\(15\) 4.14755 + 4.14755i 1.07089 + 1.07089i
\(16\) −1.60513 3.66382i −0.401283 0.915954i
\(17\) 4.75422 1.15307 0.576534 0.817073i \(-0.304405\pi\)
0.576534 + 0.817073i \(0.304405\pi\)
\(18\) −0.361232 + 1.21286i −0.0851431 + 0.285873i
\(19\) −2.62674 + 1.08803i −0.602616 + 0.249612i −0.663068 0.748559i \(-0.730746\pi\)
0.0604517 + 0.998171i \(0.480746\pi\)
\(20\) −6.67692 + 4.55967i −1.49300 + 1.01957i
\(21\) −0.224453 0.0929715i −0.0489797 0.0202881i
\(22\) −0.175861 + 0.0182187i −0.0374936 + 0.00388425i
\(23\) 0.822050 + 0.822050i 0.171409 + 0.171409i 0.787598 0.616189i \(-0.211324\pi\)
−0.616189 + 0.787598i \(0.711324\pi\)
\(24\) 3.64815 + 1.87942i 0.744675 + 0.383635i
\(25\) 8.02068 + 8.02068i 1.60414 + 1.60414i
\(26\) 5.08840 + 0.328959i 0.997917 + 0.0645142i
\(27\) −2.16258 5.22093i −0.416188 1.00477i
\(28\) 0.183229 0.280315i 0.0346270 0.0529746i
\(29\) −0.362881 + 0.876073i −0.0673854 + 0.162683i −0.953984 0.299856i \(-0.903061\pi\)
0.886599 + 0.462539i \(0.153061\pi\)
\(30\) 2.36779 7.94999i 0.432297 1.45146i
\(31\) −1.60097 + 1.60097i −0.287542 + 0.287542i −0.836108 0.548565i \(-0.815174\pi\)
0.548565 + 0.836108i \(0.315174\pi\)
\(32\) −3.47702 + 4.46210i −0.614656 + 0.788795i
\(33\) 0.128262 0.128262i 0.0223276 0.0223276i
\(34\) −3.19936 5.91349i −0.548686 1.01415i
\(35\) −0.625388 0.259044i −0.105710 0.0437864i
\(36\) 1.75169 0.366879i 0.291948 0.0611466i
\(37\) 4.11822 9.94226i 0.677031 1.63450i −0.0923646 0.995725i \(-0.529443\pi\)
0.769396 0.638772i \(-0.220557\pi\)
\(38\) 3.12101 + 2.53505i 0.506294 + 0.411240i
\(39\) −4.26493 + 3.02941i −0.682936 + 0.485094i
\(40\) 10.1647 + 5.23657i 1.60719 + 0.827975i
\(41\) 1.57976i 0.246717i 0.992362 + 0.123359i \(0.0393665\pi\)
−0.992362 + 0.123359i \(0.960633\pi\)
\(42\) 0.0354044 + 0.341749i 0.00546301 + 0.0527330i
\(43\) −2.99613 7.23329i −0.456905 1.10307i −0.969644 0.244522i \(-0.921369\pi\)
0.512739 0.858545i \(-0.328631\pi\)
\(44\) 0.141007 + 0.206482i 0.0212576 + 0.0311284i
\(45\) −1.38438 3.34218i −0.206371 0.498223i
\(46\) 0.469298 1.57570i 0.0691943 0.232324i
\(47\) 5.14120 5.14120i 0.749921 0.749921i −0.224543 0.974464i \(-0.572089\pi\)
0.974464 + 0.224543i \(0.0720889\pi\)
\(48\) −0.117333 5.80247i −0.0169355 0.837514i
\(49\) −6.97196 −0.995995
\(50\) 4.57891 15.3740i 0.647556 2.17421i
\(51\) 6.37289 + 2.63974i 0.892383 + 0.369637i
\(52\) −3.01507 6.55052i −0.418115 0.908394i
\(53\) 0.952080 + 2.29853i 0.130778 + 0.315727i 0.975682 0.219192i \(-0.0703422\pi\)
−0.844903 + 0.534919i \(0.820342\pi\)
\(54\) −5.03868 + 6.20333i −0.685678 + 0.844166i
\(55\) 0.357373 0.357373i 0.0481882 0.0481882i
\(56\) −0.471971 0.0392691i −0.0630698 0.00524755i
\(57\) −4.12519 −0.546395
\(58\) 1.33390 0.138188i 0.175149 0.0181450i
\(59\) −11.6115 4.80965i −1.51169 0.626164i −0.535787 0.844353i \(-0.679985\pi\)
−0.975906 + 0.218190i \(0.929985\pi\)
\(60\) −11.4819 + 2.40481i −1.48231 + 0.310459i
\(61\) −1.39878 + 3.37697i −0.179096 + 0.432376i −0.987777 0.155871i \(-0.950182\pi\)
0.808681 + 0.588247i \(0.200182\pi\)
\(62\) 3.06872 + 0.913973i 0.389728 + 0.116075i
\(63\) 0.105951 + 0.105951i 0.0133485 + 0.0133485i
\(64\) 7.89000 + 1.32208i 0.986250 + 0.165260i
\(65\) −11.8833 + 8.44076i −1.47394 + 1.04695i
\(66\) −0.245852 0.0732233i −0.0302623 0.00901317i
\(67\) 2.18529 + 5.27576i 0.266976 + 0.644537i 0.999338 0.0363783i \(-0.0115821\pi\)
−0.732362 + 0.680915i \(0.761582\pi\)
\(68\) −5.20242 + 7.95898i −0.630886 + 0.965168i
\(69\) 0.645497 + 1.55837i 0.0777087 + 0.187606i
\(70\) 0.0986463 + 0.952206i 0.0117905 + 0.113810i
\(71\) 12.4430i 1.47671i −0.674410 0.738357i \(-0.735602\pi\)
0.674410 0.738357i \(-0.264398\pi\)
\(72\) −1.63514 1.93193i −0.192703 0.227680i
\(73\) 8.93301 1.04553 0.522765 0.852477i \(-0.324900\pi\)
0.522765 + 0.852477i \(0.324900\pi\)
\(74\) −15.1379 + 1.56825i −1.75975 + 0.182306i
\(75\) 6.29807 + 15.2049i 0.727239 + 1.75571i
\(76\) 1.05291 5.58800i 0.120777 0.640988i
\(77\) −0.00801088 + 0.0193400i −0.000912925 + 0.00220399i
\(78\) 6.63819 + 3.26625i 0.751627 + 0.369829i
\(79\) 14.3833 1.61824 0.809122 0.587641i \(-0.199943\pi\)
0.809122 + 0.587641i \(0.199943\pi\)
\(80\) −0.326920 16.1673i −0.0365508 1.80756i
\(81\) 5.51470i 0.612744i
\(82\) 1.96497 1.06310i 0.216995 0.117400i
\(83\) −10.2392 + 4.24121i −1.12390 + 0.465533i −0.865702 0.500560i \(-0.833127\pi\)
−0.258194 + 0.966093i \(0.583127\pi\)
\(84\) 0.401255 0.274018i 0.0437806 0.0298978i
\(85\) 17.7566 + 7.35503i 1.92597 + 0.797765i
\(86\) −6.98080 + 8.59435i −0.752759 + 0.926753i
\(87\) −0.972863 + 0.972863i −0.104302 + 0.104302i
\(88\) 0.161940 0.314342i 0.0172628 0.0335090i
\(89\) 6.33972i 0.672009i −0.941860 0.336004i \(-0.890924\pi\)
0.941860 0.336004i \(-0.109076\pi\)
\(90\) −3.22552 + 3.97107i −0.340000 + 0.418588i
\(91\) 0.320941 0.511354i 0.0336437 0.0536045i
\(92\) −2.27573 + 0.476636i −0.237261 + 0.0496927i
\(93\) −3.03497 + 1.25713i −0.314712 + 0.130358i
\(94\) −9.85461 2.93505i −1.01642 0.302727i
\(95\) −11.4939 −1.17925
\(96\) −7.13838 + 4.05072i −0.728558 + 0.413425i
\(97\) −7.29863 7.29863i −0.741063 0.741063i 0.231719 0.972783i \(-0.425565\pi\)
−0.972783 + 0.231719i \(0.925565\pi\)
\(98\) 4.69179 + 8.67200i 0.473943 + 0.876004i
\(99\) −0.103356 + 0.0428116i −0.0103877 + 0.00430273i
\(100\) −22.2041 + 4.65050i −2.22041 + 0.465050i
\(101\) 4.28791 + 10.3519i 0.426663 + 1.03006i 0.980338 + 0.197323i \(0.0632249\pi\)
−0.553675 + 0.832733i \(0.686775\pi\)
\(102\) −1.00524 9.70327i −0.0995331 0.960766i
\(103\) −5.94537 + 5.94537i −0.585815 + 0.585815i −0.936495 0.350680i \(-0.885950\pi\)
0.350680 + 0.936495i \(0.385950\pi\)
\(104\) −6.11880 + 8.15845i −0.599998 + 0.800002i
\(105\) −0.694481 0.694481i −0.0677745 0.0677745i
\(106\) 2.21829 2.73103i 0.215460 0.265261i
\(107\) −17.4698 + 7.23622i −1.68887 + 0.699552i −0.999687 0.0250362i \(-0.992030\pi\)
−0.689182 + 0.724588i \(0.742030\pi\)
\(108\) 11.1067 + 2.09277i 1.06875 + 0.201377i
\(109\) −0.937189 2.26257i −0.0897664 0.216715i 0.872620 0.488400i \(-0.162419\pi\)
−0.962386 + 0.271685i \(0.912419\pi\)
\(110\) −0.685010 0.204020i −0.0653131 0.0194526i
\(111\) 11.0407 11.0407i 1.04794 1.04794i
\(112\) 0.268769 + 0.613483i 0.0253963 + 0.0579687i
\(113\) 0.849823i 0.0799447i 0.999201 + 0.0399723i \(0.0127270\pi\)
−0.999201 + 0.0399723i \(0.987273\pi\)
\(114\) 2.77605 + 5.13107i 0.260001 + 0.480569i
\(115\) 1.79853 + 4.34204i 0.167714 + 0.404897i
\(116\) −1.06953 1.56616i −0.0993035 0.145414i
\(117\) 3.14516 0.719555i 0.290770 0.0665229i
\(118\) 1.83156 + 17.6795i 0.168609 + 1.62753i
\(119\) −0.796064 −0.0729751
\(120\) 10.7180 + 12.6633i 0.978412 + 1.15600i
\(121\) 7.76712 + 7.76712i 0.706102 + 0.706102i
\(122\) 5.14172 0.532670i 0.465509 0.0482256i
\(123\) −0.877148 + 2.11762i −0.0790897 + 0.190940i
\(124\) −0.928263 4.43206i −0.0833605 0.398010i
\(125\) 9.81288 + 23.6904i 0.877691 + 2.11893i
\(126\) 0.0604859 0.203085i 0.00538852 0.0180923i
\(127\) −14.1303 −1.25387 −0.626933 0.779073i \(-0.715690\pi\)
−0.626933 + 0.779073i \(0.715690\pi\)
\(128\) −3.66513 10.7036i −0.323955 0.946073i
\(129\) 11.3596i 1.00015i
\(130\) 18.4958 + 9.10065i 1.62219 + 0.798180i
\(131\) −16.9635 7.02653i −1.48211 0.613911i −0.512528 0.858670i \(-0.671291\pi\)
−0.969584 + 0.244759i \(0.921291\pi\)
\(132\) 0.0743682 + 0.355076i 0.00647292 + 0.0309054i
\(133\) 0.439831 0.182184i 0.0381382 0.0157974i
\(134\) 5.09161 6.26849i 0.439848 0.541515i
\(135\) 22.8453i 1.96621i
\(136\) 13.4007 + 1.11496i 1.14910 + 0.0956074i
\(137\) −11.5094 −0.983314 −0.491657 0.870789i \(-0.663609\pi\)
−0.491657 + 0.870789i \(0.663609\pi\)
\(138\) 1.50397 1.85160i 0.128027 0.157619i
\(139\) 0.979057 0.405539i 0.0830425 0.0343973i −0.340776 0.940145i \(-0.610690\pi\)
0.423818 + 0.905747i \(0.360690\pi\)
\(140\) 1.11801 0.763488i 0.0944889 0.0645266i
\(141\) 9.74623 4.03702i 0.820780 0.339978i
\(142\) −15.4771 + 8.37355i −1.29881 + 0.702692i
\(143\) 0.261029 + 0.367487i 0.0218283 + 0.0307308i
\(144\) −1.30264 + 3.33395i −0.108553 + 0.277829i
\(145\) −2.71066 + 2.71066i −0.225108 + 0.225108i
\(146\) −6.01148 11.1112i −0.497514 0.919572i
\(147\) −9.34570 3.87112i −0.770821 0.319284i
\(148\) 12.1378 + 17.7738i 0.997717 + 1.46100i
\(149\) 0.776656 1.87501i 0.0636262 0.153607i −0.888869 0.458162i \(-0.848508\pi\)
0.952495 + 0.304555i \(0.0985078\pi\)
\(150\) 14.6741 18.0659i 1.19814 1.47508i
\(151\) 15.1813i 1.23544i −0.786400 0.617718i \(-0.788057\pi\)
0.786400 0.617718i \(-0.211943\pi\)
\(152\) −7.65913 + 2.45080i −0.621238 + 0.198786i
\(153\) −3.00825 3.00825i −0.243203 0.243203i
\(154\) 0.0294468 0.00305061i 0.00237289 0.000245825i
\(155\) −8.45626 + 3.50270i −0.679223 + 0.281343i
\(156\) −0.404495 10.4549i −0.0323855 0.837059i
\(157\) −1.17723 + 2.84209i −0.0939532 + 0.226823i −0.963869 0.266378i \(-0.914173\pi\)
0.869916 + 0.493201i \(0.164173\pi\)
\(158\) −9.67924 17.8905i −0.770039 1.42329i
\(159\) 3.60974i 0.286271i
\(160\) −19.8895 + 11.2864i −1.57240 + 0.892270i
\(161\) −0.137647 0.137647i −0.0108481 0.0108481i
\(162\) −6.85940 + 3.71112i −0.538925 + 0.291573i
\(163\) 10.2499 4.24566i 0.802837 0.332546i 0.0567448 0.998389i \(-0.481928\pi\)
0.746092 + 0.665843i \(0.231928\pi\)
\(164\) −2.64466 1.72869i −0.206513 0.134988i
\(165\) 0.677476 0.280620i 0.0527415 0.0218462i
\(166\) 12.1658 + 9.88177i 0.944253 + 0.766974i
\(167\) 1.63379 0.126426 0.0632132 0.998000i \(-0.479865\pi\)
0.0632132 + 0.998000i \(0.479865\pi\)
\(168\) −0.610860 0.314697i −0.0471288 0.0242794i
\(169\) −5.65246 11.7068i −0.434805 0.900525i
\(170\) −2.80086 27.0359i −0.214816 2.07356i
\(171\) 2.35054 + 0.973625i 0.179750 + 0.0744549i
\(172\) 15.3877 + 2.89942i 1.17330 + 0.221079i
\(173\) 3.26898 7.89203i 0.248536 0.600020i −0.749544 0.661955i \(-0.769727\pi\)
0.998080 + 0.0619350i \(0.0197272\pi\)
\(174\) 1.86477 + 0.555396i 0.141368 + 0.0421044i
\(175\) −1.34301 1.34301i −0.101522 0.101522i
\(176\) −0.499969 + 0.0101099i −0.0376866 + 0.000762066i
\(177\) −12.8944 12.8944i −0.969202 0.969202i
\(178\) −7.88559 + 4.26632i −0.591050 + 0.319774i
\(179\) 2.69384 + 1.11583i 0.201347 + 0.0834007i 0.481078 0.876678i \(-0.340245\pi\)
−0.279731 + 0.960078i \(0.590245\pi\)
\(180\) 7.10999 + 1.33969i 0.529948 + 0.0998548i
\(181\) 14.1781 5.87274i 1.05385 0.436518i 0.212583 0.977143i \(-0.431812\pi\)
0.841263 + 0.540625i \(0.181812\pi\)
\(182\) −0.852020 0.0550821i −0.0631559 0.00408296i
\(183\) −3.75006 + 3.75006i −0.277212 + 0.277212i
\(184\) 2.12431 + 2.50989i 0.156606 + 0.185032i
\(185\) 30.7624 30.7624i 2.26170 2.26170i
\(186\) 3.60605 + 2.92903i 0.264408 + 0.214767i
\(187\) 0.227453 0.549119i 0.0166330 0.0401556i
\(188\) 2.98094 + 14.2327i 0.217407 + 1.03803i
\(189\) 0.362110 + 0.874211i 0.0263396 + 0.0635895i
\(190\) 7.73484 + 14.2966i 0.561144 + 1.03718i
\(191\) 12.8849i 0.932318i 0.884701 + 0.466159i \(0.154363\pi\)
−0.884701 + 0.466159i \(0.845637\pi\)
\(192\) 9.84223 + 6.15306i 0.710302 + 0.444059i
\(193\) −10.8423 + 10.8423i −0.780448 + 0.780448i −0.979906 0.199458i \(-0.936082\pi\)
0.199458 + 0.979906i \(0.436082\pi\)
\(194\) −4.16670 + 13.9899i −0.299152 + 1.00442i
\(195\) −20.6158 + 4.71651i −1.47633 + 0.337757i
\(196\) 7.62923 11.6717i 0.544945 0.833691i
\(197\) −1.98865 0.823725i −0.141685 0.0586880i 0.310714 0.950503i \(-0.399432\pi\)
−0.452399 + 0.891815i \(0.649432\pi\)
\(198\) 0.122804 + 0.0997485i 0.00872734 + 0.00708882i
\(199\) 3.15196 3.15196i 0.223437 0.223437i −0.586507 0.809944i \(-0.699497\pi\)
0.809944 + 0.586507i \(0.199497\pi\)
\(200\) 20.7268 + 24.4888i 1.46560 + 1.73162i
\(201\) 8.28536i 0.584405i
\(202\) 9.99059 12.2998i 0.702935 0.865413i
\(203\) 0.0607622 0.146693i 0.00426467 0.0102958i
\(204\) −11.3928 + 7.78018i −0.797658 + 0.544721i
\(205\) −2.44397 + 5.90027i −0.170694 + 0.412093i
\(206\) 11.3960 + 3.39414i 0.794000 + 0.236481i
\(207\) 1.04031i 0.0723066i
\(208\) 14.2655 + 2.12057i 0.989131 + 0.147035i
\(209\) 0.355446i 0.0245867i
\(210\) −0.396471 + 1.33118i −0.0273591 + 0.0918599i
\(211\) −5.28688 + 12.7637i −0.363964 + 0.878687i 0.630748 + 0.775987i \(0.282748\pi\)
−0.994712 + 0.102699i \(0.967252\pi\)
\(212\) −4.88977 0.921349i −0.335831 0.0632785i
\(213\) 6.90887 16.6795i 0.473388 1.14286i
\(214\) 20.7570 + 16.8600i 1.41892 + 1.15253i
\(215\) 31.6509i 2.15857i
\(216\) −4.87122 15.2233i −0.331444 1.03582i
\(217\) 0.268072 0.268072i 0.0181979 0.0181979i
\(218\) −2.18360 + 2.68831i −0.147892 + 0.182076i
\(219\) 11.9744 + 4.95997i 0.809157 + 0.335164i
\(220\) 0.207210 + 0.989338i 0.0139701 + 0.0667012i
\(221\) −9.11245 + 14.5189i −0.612970 + 0.976644i
\(222\) −21.1627 6.30300i −1.42035 0.423030i
\(223\) 11.4720 11.4720i 0.768222 0.768222i −0.209571 0.977793i \(-0.567207\pi\)
0.977793 + 0.209571i \(0.0672068\pi\)
\(224\) 0.582205 0.747150i 0.0389002 0.0499211i
\(225\) 10.1502i 0.676682i
\(226\) 1.05704 0.571890i 0.0703135 0.0380415i
\(227\) 5.41538 + 13.0739i 0.359431 + 0.867744i 0.995380 + 0.0960125i \(0.0306089\pi\)
−0.635949 + 0.771731i \(0.719391\pi\)
\(228\) 4.51408 6.90592i 0.298952 0.457356i
\(229\) 4.07204 9.83077i 0.269088 0.649635i −0.730353 0.683070i \(-0.760644\pi\)
0.999441 + 0.0334344i \(0.0106445\pi\)
\(230\) 4.19048 5.15907i 0.276312 0.340179i
\(231\) −0.0214767 + 0.0214767i −0.00141306 + 0.00141306i
\(232\) −1.22831 + 2.38427i −0.0806423 + 0.156535i
\(233\) −7.99196 + 7.99196i −0.523571 + 0.523571i −0.918648 0.395077i \(-0.870718\pi\)
0.395077 + 0.918648i \(0.370718\pi\)
\(234\) −3.01155 3.42785i −0.196871 0.224086i
\(235\) 27.1556 11.2482i 1.77144 0.733754i
\(236\) 20.7580 14.1756i 1.35123 0.922756i
\(237\) 19.2803 + 7.98617i 1.25239 + 0.518758i
\(238\) 0.535712 + 0.990176i 0.0347251 + 0.0641836i
\(239\) −0.518131 0.518131i −0.0335151 0.0335151i 0.690151 0.723666i \(-0.257544\pi\)
−0.723666 + 0.690151i \(0.757544\pi\)
\(240\) 8.53850 21.8532i 0.551158 1.41062i
\(241\) 10.3809 + 10.3809i 0.668691 + 0.668691i 0.957413 0.288722i \(-0.0932304\pi\)
−0.288722 + 0.957413i \(0.593230\pi\)
\(242\) 4.43416 14.8879i 0.285038 0.957034i
\(243\) −3.42575 + 8.27049i −0.219762 + 0.530552i
\(244\) −4.12268 6.03701i −0.263928 0.386480i
\(245\) −26.0397 10.7860i −1.66361 0.689092i
\(246\) 3.22426 0.334026i 0.205571 0.0212967i
\(247\) 1.71197 10.1072i 0.108930 0.643107i
\(248\) −4.88809 + 4.13717i −0.310394 + 0.262710i
\(249\) −16.0802 −1.01904
\(250\) 22.8635 28.1481i 1.44601 1.78024i
\(251\) 26.6225 11.0274i 1.68040 0.696044i 0.681053 0.732234i \(-0.261522\pi\)
0.999345 + 0.0361906i \(0.0115223\pi\)
\(252\) −0.293309 + 0.0614316i −0.0184768 + 0.00386983i
\(253\) 0.134277 0.0556192i 0.00844190 0.00349675i
\(254\) 9.50903 + 17.5759i 0.596650 + 1.10281i
\(255\) 19.7184 + 19.7184i 1.23481 + 1.23481i
\(256\) −10.8471 + 11.7618i −0.677943 + 0.735114i
\(257\) 1.49040i 0.0929688i −0.998919 0.0464844i \(-0.985198\pi\)
0.998919 0.0464844i \(-0.0148018\pi\)
\(258\) −14.1295 + 7.64444i −0.879664 + 0.475922i
\(259\) −0.689570 + 1.66477i −0.0428478 + 0.103444i
\(260\) −1.12703 29.1301i −0.0698956 1.80657i
\(261\) 0.783953 0.324724i 0.0485255 0.0200999i
\(262\) 2.67577 + 25.8284i 0.165309 + 1.59569i
\(263\) 20.6831 + 20.6831i 1.27537 + 1.27537i 0.943228 + 0.332146i \(0.107773\pi\)
0.332146 + 0.943228i \(0.392227\pi\)
\(264\) 0.391611 0.331451i 0.0241020 0.0203994i
\(265\) 10.0577i 0.617840i
\(266\) −0.522593 0.424479i −0.0320422 0.0260265i
\(267\) 3.52007 8.49820i 0.215425 0.520081i
\(268\) −11.2234 2.11476i −0.685578 0.129179i
\(269\) 6.23575 + 2.58293i 0.380200 + 0.157484i 0.564595 0.825368i \(-0.309032\pi\)
−0.184395 + 0.982852i \(0.559032\pi\)
\(270\) −28.4159 + 15.3738i −1.72934 + 0.935620i
\(271\) −13.7184 + 13.7184i −0.833333 + 0.833333i −0.987971 0.154638i \(-0.950579\pi\)
0.154638 + 0.987971i \(0.450579\pi\)
\(272\) −7.63116 17.4186i −0.462707 1.05616i
\(273\) 0.714136 0.507255i 0.0432215 0.0307005i
\(274\) 7.74526 + 14.3158i 0.467908 + 0.864852i
\(275\) 1.31013 0.542672i 0.0790036 0.0327244i
\(276\) −3.31519 0.624662i −0.199551 0.0376002i
\(277\) −24.3471 + 10.0849i −1.46287 + 0.605942i −0.965221 0.261435i \(-0.915804\pi\)
−0.497652 + 0.867377i \(0.665804\pi\)
\(278\) −1.16328 0.944882i −0.0697690 0.0566702i
\(279\) 2.02604 0.121296
\(280\) −1.70202 0.876831i −0.101715 0.0524007i
\(281\) 31.9260i 1.90455i −0.305245 0.952274i \(-0.598738\pi\)
0.305245 0.952274i \(-0.401262\pi\)
\(282\) −11.5801 9.40602i −0.689587 0.560121i
\(283\) 16.4236 6.80289i 0.976283 0.404390i 0.163235 0.986587i \(-0.447807\pi\)
0.813047 + 0.582198i \(0.197807\pi\)
\(284\) 20.8307 + 13.6161i 1.23607 + 0.807965i
\(285\) −15.4072 6.38188i −0.912645 0.378030i
\(286\) 0.281436 0.571979i 0.0166416 0.0338218i
\(287\) 0.264521i 0.0156142i
\(288\) 5.02351 0.623310i 0.296013 0.0367289i
\(289\) 5.60262 0.329566
\(290\) 5.19577 + 1.54748i 0.305106 + 0.0908714i
\(291\) −5.73109 13.8361i −0.335963 0.811085i
\(292\) −9.77516 + 14.9546i −0.572048 + 0.875154i
\(293\) −2.21139 + 5.33878i −0.129191 + 0.311895i −0.975218 0.221245i \(-0.928988\pi\)
0.846027 + 0.533140i \(0.178988\pi\)
\(294\) 1.47416 + 14.2296i 0.0859745 + 0.829889i
\(295\) −35.9273 35.9273i −2.09177 2.09177i
\(296\) 13.9396 27.0583i 0.810225 1.57273i
\(297\) −0.706487 −0.0409945
\(298\) −2.85487 + 0.295758i −0.165378 + 0.0171328i
\(299\) −4.08608 + 0.934818i −0.236304 + 0.0540619i
\(300\) −32.3461 6.09478i −1.86750 0.351882i
\(301\) 0.501682 + 1.21117i 0.0289165 + 0.0698106i
\(302\) −18.8831 + 10.2163i −1.08660 + 0.587880i
\(303\) 16.2573i 0.933956i
\(304\) 8.20262 + 7.87747i 0.470453 + 0.451804i
\(305\) −10.4487 + 10.4487i −0.598290 + 0.598290i
\(306\) −1.71737 + 5.76619i −0.0981758 + 0.329631i
\(307\) 9.08120 + 21.9239i 0.518291 + 1.25127i 0.938952 + 0.344048i \(0.111798\pi\)
−0.420661 + 0.907218i \(0.638202\pi\)
\(308\) −0.0236107 0.0345741i −0.00134535 0.00197004i
\(309\) −11.2707 + 4.66848i −0.641168 + 0.265581i
\(310\) 10.0474 + 8.16108i 0.570656 + 0.463518i
\(311\) 16.0453 + 16.0453i 0.909848 + 0.909848i 0.996259 0.0864119i \(-0.0275401\pi\)
−0.0864119 + 0.996259i \(0.527540\pi\)
\(312\) −12.7320 + 7.53874i −0.720806 + 0.426797i
\(313\) 3.40491 3.40491i 0.192457 0.192457i −0.604300 0.796757i \(-0.706547\pi\)
0.796757 + 0.604300i \(0.206547\pi\)
\(314\) 4.32732 0.448300i 0.244205 0.0252990i
\(315\) 0.231805 + 0.559628i 0.0130608 + 0.0315314i
\(316\) −15.7392 + 24.0788i −0.885400 + 1.35454i
\(317\) −24.2852 + 10.0593i −1.36399 + 0.564984i −0.940153 0.340753i \(-0.889318\pi\)
−0.423840 + 0.905737i \(0.639318\pi\)
\(318\) 4.48993 2.42918i 0.251783 0.136222i
\(319\) 0.0838266 + 0.0838266i 0.00469339 + 0.00469339i
\(320\) 27.4231 + 17.1441i 1.53300 + 0.958385i
\(321\) −27.4356 −1.53130
\(322\) −0.0785811 + 0.263841i −0.00437915 + 0.0147033i
\(323\) −12.4881 + 5.17275i −0.694857 + 0.287819i
\(324\) 9.23208 + 6.03459i 0.512894 + 0.335255i
\(325\) −39.8676 + 9.12096i −2.21145 + 0.505940i
\(326\) −12.1786 9.89215i −0.674512 0.547876i
\(327\) 3.55328i 0.196497i
\(328\) −0.370487 + 4.45285i −0.0204567 + 0.245868i
\(329\) −0.860862 + 0.860862i −0.0474608 + 0.0474608i
\(330\) −0.804955 0.653828i −0.0443113 0.0359921i
\(331\) −12.5662 5.20508i −0.690700 0.286097i 0.00959195 0.999954i \(-0.496947\pi\)
−0.700292 + 0.713857i \(0.746947\pi\)
\(332\) 4.10431 21.7823i 0.225253 1.19546i
\(333\) −8.89682 + 3.68518i −0.487543 + 0.201947i
\(334\) −1.09946 2.03217i −0.0601598 0.111196i
\(335\) 23.0853i 1.26128i
\(336\) 0.0196466 + 0.971587i 0.00107181 + 0.0530044i
\(337\) 4.69307 0.255648 0.127824 0.991797i \(-0.459201\pi\)
0.127824 + 0.991797i \(0.459201\pi\)
\(338\) −10.7576 + 14.9089i −0.585135 + 0.810936i
\(339\) −0.471856 + 1.13916i −0.0256277 + 0.0618708i
\(340\) −31.7435 + 21.6777i −1.72153 + 1.17564i
\(341\) 0.108320 + 0.261508i 0.00586586 + 0.0141614i
\(342\) −0.370765 3.57889i −0.0200487 0.193524i
\(343\) 2.33952 0.126322
\(344\) −6.74879 21.0910i −0.363870 1.13715i
\(345\) 6.81899i 0.367122i
\(346\) −12.0163 + 1.24486i −0.645999 + 0.0669240i
\(347\) 11.0734 + 26.7334i 0.594449 + 1.43513i 0.879167 + 0.476515i \(0.158100\pi\)
−0.284718 + 0.958611i \(0.591900\pi\)
\(348\) −0.564079 2.69323i −0.0302378 0.144373i
\(349\) −5.53227 13.3561i −0.296135 0.714934i −0.999989 0.00458953i \(-0.998539\pi\)
0.703854 0.710345i \(-0.251461\pi\)
\(350\) −0.766710 + 2.57427i −0.0409824 + 0.137601i
\(351\) 20.0892 + 3.40272i 1.07228 + 0.181624i
\(352\) 0.349030 + 0.615078i 0.0186034 + 0.0327837i
\(353\) −15.0043 15.0043i −0.798600 0.798600i 0.184275 0.982875i \(-0.441006\pi\)
−0.982875 + 0.184275i \(0.941006\pi\)
\(354\) −7.36125 + 24.7159i −0.391246 + 1.31363i
\(355\) 19.2500 46.4736i 1.02168 2.46656i
\(356\) 10.6132 + 6.93738i 0.562501 + 0.367681i
\(357\) −1.06710 0.442007i −0.0564769 0.0233935i
\(358\) −0.424916 4.10160i −0.0224575 0.216776i
\(359\) 6.78539 0.358119 0.179060 0.983838i \(-0.442694\pi\)
0.179060 + 0.983838i \(0.442694\pi\)
\(360\) −3.11832 9.74524i −0.164350 0.513619i
\(361\) −7.71907 + 7.71907i −0.406267 + 0.406267i
\(362\) −16.8459 13.6832i −0.885400 0.719171i
\(363\) 6.09897 + 14.7242i 0.320113 + 0.772821i
\(364\) 0.504855 + 1.09684i 0.0264616 + 0.0574902i
\(365\) 33.3640 + 13.8198i 1.74635 + 0.723363i
\(366\) 7.18808 + 2.14086i 0.375727 + 0.111905i
\(367\) 7.20556 0.376127 0.188064 0.982157i \(-0.439779\pi\)
0.188064 + 0.982157i \(0.439779\pi\)
\(368\) 1.69234 4.33134i 0.0882193 0.225787i
\(369\) 0.999600 0.999600i 0.0520371 0.0520371i
\(370\) −58.9651 17.5619i −3.06545 0.912999i
\(371\) −0.159420 0.384874i −0.00827667 0.0199816i
\(372\) 1.21655 6.45644i 0.0630751 0.334751i
\(373\) −12.2576 29.5926i −0.634677 1.53225i −0.833681 0.552246i \(-0.813771\pi\)
0.199004 0.979999i \(-0.436229\pi\)
\(374\) −0.836081 + 0.0866160i −0.0432327 + 0.00447880i
\(375\) 37.2048i 1.92125i
\(376\) 15.6972 13.2857i 0.809519 0.685159i
\(377\) −1.97989 2.78738i −0.101970 0.143557i
\(378\) 0.843696 1.03871i 0.0433950 0.0534254i
\(379\) 5.46338 13.1898i 0.280635 0.677513i −0.719216 0.694787i \(-0.755499\pi\)
0.999851 + 0.0172737i \(0.00549867\pi\)
\(380\) 12.5775 19.2418i 0.645210 0.987083i
\(381\) −18.9413 7.84574i −0.970392 0.401950i
\(382\) 16.0267 8.67090i 0.819999 0.443642i
\(383\) 2.96879 2.96879i 0.151698 0.151698i −0.627178 0.778876i \(-0.715790\pi\)
0.778876 + 0.627178i \(0.215790\pi\)
\(384\) 1.03008 16.3829i 0.0525659 0.836035i
\(385\) −0.0598399 + 0.0598399i −0.00304972 + 0.00304972i
\(386\) 20.7825 + 6.18976i 1.05780 + 0.315050i
\(387\) −2.68108 + 6.47270i −0.136287 + 0.329026i
\(388\) 20.2052 4.23184i 1.02576 0.214839i
\(389\) 14.2653 + 34.4396i 0.723281 + 1.74616i 0.663781 + 0.747927i \(0.268951\pi\)
0.0595006 + 0.998228i \(0.481049\pi\)
\(390\) 19.7400 + 22.4688i 0.999575 + 1.13775i
\(391\) 3.90821 + 3.90821i 0.197647 + 0.197647i
\(392\) −19.6518 1.63507i −0.992565 0.0825836i
\(393\) −18.8377 18.8377i −0.950236 0.950236i
\(394\) 0.313682 + 3.02789i 0.0158031 + 0.152543i
\(395\) 53.7203 + 22.2517i 2.70296 + 1.11960i
\(396\) 0.0414297 0.219875i 0.00208192 0.0110491i
\(397\) −2.02722 + 0.839703i −0.101743 + 0.0421435i −0.432975 0.901406i \(-0.642536\pi\)
0.331231 + 0.943550i \(0.392536\pi\)
\(398\) −6.04165 1.79942i −0.302840 0.0901966i
\(399\) 0.690737 0.0345801
\(400\) 16.5120 42.2606i 0.825602 2.11303i
\(401\) −1.35223 1.35223i −0.0675272 0.0675272i 0.672537 0.740064i \(-0.265205\pi\)
−0.740064 + 0.672537i \(0.765205\pi\)
\(402\) 10.3057 5.57565i 0.514000 0.278088i
\(403\) −1.82059 7.95776i −0.0906900 0.396404i
\(404\) −22.0222 4.14951i −1.09564 0.206446i
\(405\) 8.53153 20.5969i 0.423935 1.02347i
\(406\) −0.223352 + 0.0231388i −0.0110848 + 0.00114836i
\(407\) −0.951320 0.951320i −0.0471552 0.0471552i
\(408\) 17.3441 + 8.93517i 0.858661 + 0.442357i
\(409\) 23.2371 1.14900 0.574501 0.818504i \(-0.305196\pi\)
0.574501 + 0.818504i \(0.305196\pi\)
\(410\) 8.98367 0.930686i 0.443672 0.0459633i
\(411\) −15.4280 6.39049i −0.761007 0.315219i
\(412\) −3.44721 16.4589i −0.169832 0.810874i
\(413\) 1.94428 + 0.805346i 0.0956717 + 0.0396285i
\(414\) −1.29398 + 0.700078i −0.0635956 + 0.0344070i
\(415\) −44.8038 −2.19933
\(416\) −6.96231 19.1710i −0.341355 0.939934i
\(417\) 1.53757 0.0752950
\(418\) 0.442118 0.239198i 0.0216247 0.0116996i
\(419\) 5.64401 + 2.33783i 0.275728 + 0.114210i 0.516263 0.856430i \(-0.327323\pi\)
−0.240535 + 0.970641i \(0.577323\pi\)
\(420\) 1.92257 0.402670i 0.0938120 0.0196483i
\(421\) 15.9719 + 6.61577i 0.778422 + 0.322433i 0.736279 0.676679i \(-0.236581\pi\)
0.0421436 + 0.999112i \(0.486581\pi\)
\(422\) 19.4338 2.01329i 0.946021 0.0980055i
\(423\) −6.50623 −0.316344
\(424\) 2.14456 + 6.70211i 0.104149 + 0.325483i
\(425\) 38.1321 + 38.1321i 1.84968 + 1.84968i
\(426\) −25.3959 + 2.63096i −1.23044 + 0.127470i
\(427\) 0.234218 0.565452i 0.0113346 0.0273641i
\(428\) 7.00265 37.1644i 0.338486 1.79641i
\(429\) 0.145857 + 0.637539i 0.00704205 + 0.0307807i
\(430\) −39.3686 + 21.2995i −1.89852 + 1.02715i
\(431\) −4.74711 4.74711i −0.228660 0.228660i 0.583472 0.812133i \(-0.301694\pi\)
−0.812133 + 0.583472i \(0.801694\pi\)
\(432\) −15.6573 + 16.3036i −0.753312 + 0.784406i
\(433\) 35.3538 1.69899 0.849497 0.527593i \(-0.176906\pi\)
0.849497 + 0.527593i \(0.176906\pi\)
\(434\) −0.513838 0.153039i −0.0246650 0.00734611i
\(435\) −5.13863 + 2.12849i −0.246378 + 0.102053i
\(436\) 4.81329 + 0.906938i 0.230515 + 0.0434345i
\(437\) −3.05373 1.26490i −0.146080 0.0605082i
\(438\) −1.88880 18.2321i −0.0902504 0.871163i
\(439\) 21.1592 + 21.1592i 1.00988 + 1.00988i 0.999951 + 0.00992460i \(0.00315915\pi\)
0.00992460 + 0.999951i \(0.496841\pi\)
\(440\) 1.09114 0.923512i 0.0520178 0.0440267i
\(441\) 4.41154 + 4.41154i 0.210073 + 0.210073i
\(442\) 24.1914 + 1.56394i 1.15067 + 0.0743893i
\(443\) 7.27080 + 17.5533i 0.345446 + 0.833980i 0.997146 + 0.0755033i \(0.0240563\pi\)
−0.651700 + 0.758477i \(0.725944\pi\)
\(444\) 6.40155 + 30.5646i 0.303804 + 1.45053i
\(445\) 9.80788 23.6783i 0.464938 1.12246i
\(446\) −21.9894 6.54923i −1.04123 0.310115i
\(447\) 2.08217 2.08217i 0.0984832 0.0984832i
\(448\) −1.32113 0.221374i −0.0624176 0.0104590i
\(449\) −10.5786 + 10.5786i −0.499236 + 0.499236i −0.911200 0.411964i \(-0.864843\pi\)
0.411964 + 0.911200i \(0.364843\pi\)
\(450\) −12.6253 + 6.83061i −0.595160 + 0.321998i
\(451\) 0.182465 + 0.0755793i 0.00859192 + 0.00355889i
\(452\) −1.42268 0.929939i −0.0669171 0.0437406i
\(453\) 8.42927 20.3501i 0.396042 0.956129i
\(454\) 12.6175 15.5339i 0.592169 0.729044i
\(455\) 1.98978 1.41335i 0.0932822 0.0662590i
\(456\) −11.6276 0.967443i −0.544513 0.0453047i
\(457\) 8.47358i 0.396377i −0.980164 0.198189i \(-0.936494\pi\)
0.980164 0.198189i \(-0.0635059\pi\)
\(458\) −14.9682 + 1.55067i −0.699417 + 0.0724579i
\(459\) −10.2814 24.8214i −0.479894 1.15857i
\(460\) −9.23704 1.74048i −0.430679 0.0811502i
\(461\) 8.14766 + 19.6702i 0.379474 + 0.916132i 0.992064 + 0.125731i \(0.0401277\pi\)
−0.612590 + 0.790401i \(0.709872\pi\)
\(462\) 0.0411663 + 0.0122608i 0.00191523 + 0.000570423i
\(463\) 18.4109 18.4109i 0.855627 0.855627i −0.135193 0.990819i \(-0.543165\pi\)
0.990819 + 0.135193i \(0.0431653\pi\)
\(464\) 3.79224 0.0766835i 0.176050 0.00355994i
\(465\) −13.2802 −0.615854
\(466\) 15.3189 + 4.56251i 0.709635 + 0.211354i
\(467\) −33.8363 14.0155i −1.56576 0.648559i −0.579681 0.814844i \(-0.696823\pi\)
−0.986078 + 0.166285i \(0.946823\pi\)
\(468\) −2.23707 + 6.05267i −0.103409 + 0.279785i
\(469\) −0.365913 0.883393i −0.0168963 0.0407913i
\(470\) −32.2654 26.2078i −1.48829 1.20887i
\(471\) −3.15608 + 3.15608i −0.145425 + 0.145425i
\(472\) −31.6013 16.2801i −1.45457 0.749351i
\(473\) −0.978796 −0.0450051
\(474\) −3.04120 29.3559i −0.139687 1.34836i
\(475\) −29.7950 12.3415i −1.36709 0.566267i
\(476\) 0.871112 1.33268i 0.0399273 0.0610833i
\(477\) 0.851968 2.05683i 0.0390089 0.0941759i
\(478\) −0.295795 + 0.993149i −0.0135293 + 0.0454256i
\(479\) 8.74720 + 8.74720i 0.399670 + 0.399670i 0.878117 0.478447i \(-0.158800\pi\)
−0.478447 + 0.878117i \(0.658800\pi\)
\(480\) −32.9279 + 4.08565i −1.50295 + 0.186484i
\(481\) 22.4691 + 31.6330i 1.02450 + 1.44234i
\(482\) 5.92631 19.8980i 0.269936 0.906327i
\(483\) −0.108084 0.260939i −0.00491801 0.0118731i
\(484\) −21.5022 + 4.50348i −0.977372 + 0.204704i
\(485\) −15.9684 38.5511i −0.725087 1.75052i
\(486\) 12.5925 1.30456i 0.571209 0.0591759i
\(487\) 25.0041i 1.13304i 0.824047 + 0.566522i \(0.191711\pi\)
−0.824047 + 0.566522i \(0.808289\pi\)
\(488\) −4.73471 + 9.19057i −0.214330 + 0.416037i
\(489\) 16.0971 0.727936
\(490\) 4.10740 + 39.6476i 0.185553 + 1.79110i
\(491\) 8.43661 + 20.3678i 0.380739 + 0.919184i 0.991823 + 0.127619i \(0.0407335\pi\)
−0.611085 + 0.791565i \(0.709266\pi\)
\(492\) −2.58524 3.78568i −0.116552 0.170672i
\(493\) −1.72522 + 4.16505i −0.0776999 + 0.187584i
\(494\) −13.7238 + 4.67225i −0.617464 + 0.210214i
\(495\) −0.452259 −0.0203275
\(496\) 8.43542 + 3.29588i 0.378761 + 0.147990i
\(497\) 2.08351i 0.0934580i
\(498\) 10.8212 + 20.0012i 0.484909 + 0.896274i
\(499\) −7.73492 + 3.20391i −0.346263 + 0.143427i −0.549035 0.835799i \(-0.685005\pi\)
0.202773 + 0.979226i \(0.435005\pi\)
\(500\) −50.3978 9.49614i −2.25386 0.424680i
\(501\) 2.19005 + 0.907147i 0.0978440 + 0.0405283i
\(502\) −31.6320 25.6932i −1.41180 1.14674i
\(503\) 4.00991 4.00991i 0.178793 0.178793i −0.612036 0.790830i \(-0.709649\pi\)
0.790830 + 0.612036i \(0.209649\pi\)
\(504\) 0.273794 + 0.323489i 0.0121958 + 0.0144094i
\(505\) 45.2972i 2.01570i
\(506\) −0.159543 0.129590i −0.00709255 0.00576096i
\(507\) −1.07685 18.8311i −0.0478245 0.836319i
\(508\) 15.4625 23.6554i 0.686035 1.04954i
\(509\) 24.6008 10.1900i 1.09041 0.451664i 0.236262 0.971689i \(-0.424078\pi\)
0.854151 + 0.520026i \(0.174078\pi\)
\(510\) 11.2570 37.7960i 0.498468 1.67364i
\(511\) −1.49578 −0.0661693
\(512\) 21.9294 + 5.57691i 0.969151 + 0.246467i
\(513\) 11.3611 + 11.3611i 0.501604 + 0.501604i
\(514\) −1.85382 + 1.00297i −0.0817686 + 0.0442391i
\(515\) −31.4033 + 13.0077i −1.38379 + 0.573186i
\(516\) 19.0169 + 12.4305i 0.837173 + 0.547221i
\(517\) −0.347849 0.839782i −0.0152984 0.0369336i
\(518\) 2.53475 0.262594i 0.111371 0.0115377i
\(519\) 8.76395 8.76395i 0.384695 0.384695i
\(520\) −35.4747 + 21.0050i −1.55567 + 0.921130i
\(521\) 23.9151 + 23.9151i 1.04774 + 1.04774i 0.998802 + 0.0489379i \(0.0155836\pi\)
0.0489379 + 0.998802i \(0.484416\pi\)
\(522\) −0.931467 0.756588i −0.0407692 0.0331150i
\(523\) −15.2407 + 6.31292i −0.666431 + 0.276045i −0.690142 0.723674i \(-0.742452\pi\)
0.0237112 + 0.999719i \(0.492452\pi\)
\(524\) 30.3258 20.7095i 1.32479 0.904699i
\(525\) −1.05457 2.54596i −0.0460253 0.111115i
\(526\) 11.8077 39.6451i 0.514841 1.72861i
\(527\) −7.61136 + 7.61136i −0.331556 + 0.331556i
\(528\) −0.675807 0.264051i −0.0294107 0.0114913i
\(529\) 21.6485i 0.941238i
\(530\) 12.5102 6.76835i 0.543408 0.293998i
\(531\) 4.30391 + 10.3906i 0.186774 + 0.450912i
\(532\) −0.176304 + 0.935675i −0.00764373 + 0.0405667i
\(533\) −4.82441 3.02794i −0.208969 0.131155i
\(534\) −12.9392 + 1.34047i −0.559935 + 0.0580080i
\(535\) −76.4430 −3.30492
\(536\) 4.92238 + 15.3832i 0.212614 + 0.664454i
\(537\) 2.99146 + 2.99146i 0.129091 + 0.129091i
\(538\) −0.983603 9.49446i −0.0424061 0.409335i
\(539\) −0.333554 + 0.805271i −0.0143672 + 0.0346855i
\(540\) 38.2451 + 24.9990i 1.64581 + 1.07579i
\(541\) 6.33914 + 15.3040i 0.272541 + 0.657972i 0.999591 0.0286128i \(-0.00910898\pi\)
−0.727050 + 0.686585i \(0.759109\pi\)
\(542\) 26.2953 + 7.83167i 1.12948 + 0.336399i
\(543\) 22.2660 0.955527
\(544\) −16.5305 + 21.2138i −0.708741 + 0.909534i
\(545\) 9.90040i 0.424087i
\(546\) −1.11152 0.546912i −0.0475688 0.0234057i
\(547\) 14.7496 + 6.10949i 0.630648 + 0.261223i 0.675028 0.737792i \(-0.264131\pi\)
−0.0443805 + 0.999015i \(0.514131\pi\)
\(548\) 12.5944 19.2677i 0.538007 0.823077i
\(549\) 3.02187 1.25170i 0.128970 0.0534213i
\(550\) −1.55665 1.26440i −0.0663757 0.0539140i
\(551\) 2.69605i 0.114855i
\(552\) 1.45399 + 4.54394i 0.0618857 + 0.193403i
\(553\) −2.40839 −0.102415
\(554\) 28.9284 + 23.4972i 1.22905 + 0.998300i
\(555\) 58.3166 24.1555i 2.47540 1.02534i
\(556\) −0.392449 + 2.08280i −0.0166435 + 0.0883302i
\(557\) −35.1809 + 14.5724i −1.49066 + 0.617453i −0.971461 0.237198i \(-0.923771\pi\)
−0.519202 + 0.854651i \(0.673771\pi\)
\(558\) −1.36342 2.52006i −0.0577184 0.106683i
\(559\) 27.8324 + 4.71427i 1.17718 + 0.199392i
\(560\) 0.0547408 + 2.70711i 0.00231322 + 0.114396i
\(561\) 0.609787 0.609787i 0.0257452 0.0257452i
\(562\) −39.7109 + 21.4847i −1.67510 + 0.906276i
\(563\) 19.8298 + 8.21375i 0.835725 + 0.346168i 0.759166 0.650897i \(-0.225607\pi\)
0.0765582 + 0.997065i \(0.475607\pi\)
\(564\) −3.90671 + 20.7336i −0.164502 + 0.873043i
\(565\) −1.31472 + 3.17402i −0.0553107 + 0.133532i
\(566\) −19.5140 15.8503i −0.820234 0.666239i
\(567\) 0.923401i 0.0387792i
\(568\) 2.91815 35.0730i 0.122443 1.47163i
\(569\) −19.2787 19.2787i −0.808204 0.808204i 0.176158 0.984362i \(-0.443633\pi\)
−0.984362 + 0.176158i \(0.943633\pi\)
\(570\) 2.43028 + 23.4588i 0.101793 + 0.982582i
\(571\) 9.20125 3.81128i 0.385060 0.159497i −0.181752 0.983344i \(-0.558177\pi\)
0.566812 + 0.823847i \(0.308177\pi\)
\(572\) −0.900842 + 0.0348532i −0.0376661 + 0.00145729i
\(573\) −7.15422 + 17.2718i −0.298872 + 0.721540i
\(574\) −0.329022 + 0.178010i −0.0137331 + 0.00742998i
\(575\) 13.1868i 0.549928i
\(576\) −4.15587 5.82898i −0.173161 0.242874i
\(577\) −13.8986 13.8986i −0.578607 0.578607i 0.355912 0.934519i \(-0.384170\pi\)
−0.934519 + 0.355912i \(0.884170\pi\)
\(578\) −3.77029 6.96876i −0.156823 0.289862i
\(579\) −20.5539 + 8.51372i −0.854192 + 0.353818i
\(580\) −1.57168 7.50409i −0.0652604 0.311590i
\(581\) 1.71449 0.710163i 0.0711288 0.0294625i
\(582\) −13.3531 + 16.4396i −0.553505 + 0.681442i
\(583\) 0.311033 0.0128817
\(584\) 25.1794 + 2.09498i 1.04193 + 0.0866909i
\(585\) 12.8601 + 2.17826i 0.531700 + 0.0900598i
\(586\) 8.12874 0.842118i 0.335795 0.0347876i
\(587\) −14.4697 5.99353i −0.597226 0.247379i 0.0635297 0.997980i \(-0.479764\pi\)
−0.660756 + 0.750601i \(0.729764\pi\)
\(588\) 16.7073 11.4095i 0.688999 0.470518i
\(589\) 2.46343 5.94724i 0.101504 0.245052i
\(590\) −20.5105 + 68.8651i −0.844403 + 2.83513i
\(591\) −2.20836 2.20836i −0.0908396 0.0908396i
\(592\) −43.0369 + 0.870255i −1.76881 + 0.0357673i
\(593\) −33.8721 33.8721i −1.39096 1.39096i −0.823178 0.567783i \(-0.807801\pi\)
−0.567783 0.823178i \(-0.692199\pi\)
\(594\) 0.475431 + 0.878756i 0.0195072 + 0.0360558i
\(595\) −2.97323 1.23155i −0.121891 0.0504887i
\(596\) 2.28906 + 3.35197i 0.0937637 + 0.137302i
\(597\) 5.97520 2.47501i 0.244549 0.101295i
\(598\) 3.91250 + 4.45334i 0.159994 + 0.182110i
\(599\) 24.6953 24.6953i 1.00902 1.00902i 0.00906172 0.999959i \(-0.497116\pi\)
0.999959 0.00906172i \(-0.00288448\pi\)
\(600\) 14.1864 + 44.3349i 0.579159 + 1.80996i
\(601\) −20.4462 + 20.4462i −0.834017 + 0.834017i −0.988064 0.154047i \(-0.950769\pi\)
0.154047 + 0.988064i \(0.450769\pi\)
\(602\) 1.16889 1.43907i 0.0476405 0.0586521i
\(603\) 1.95551 4.72101i 0.0796344 0.192254i
\(604\) 25.4148 + 16.6125i 1.03411 + 0.675952i
\(605\) 16.9934 + 41.0257i 0.690880 + 1.66793i
\(606\) 20.2214 10.9404i 0.821440 0.444422i
\(607\) 27.1619i 1.10247i −0.834351 0.551234i \(-0.814157\pi\)
0.834351 0.551234i \(-0.185843\pi\)
\(608\) 4.27834 15.5039i 0.173509 0.628766i
\(609\) 0.162900 0.162900i 0.00660103 0.00660103i
\(610\) 20.0279 + 5.96503i 0.810908 + 0.241517i
\(611\) 5.84647 + 25.5548i 0.236523 + 1.03384i
\(612\) 8.32792 1.74423i 0.336636 0.0705061i
\(613\) 21.2696 + 8.81016i 0.859071 + 0.355839i 0.768344 0.640037i \(-0.221081\pi\)
0.0907270 + 0.995876i \(0.471081\pi\)
\(614\) 21.1587 26.0493i 0.853894 1.05126i
\(615\) −6.55214 + 6.55214i −0.264208 + 0.264208i
\(616\) −0.0271158 + 0.0526346i −0.00109253 + 0.00212071i
\(617\) 21.2107i 0.853909i −0.904273 0.426954i \(-0.859586\pi\)
0.904273 0.426954i \(-0.140414\pi\)
\(618\) 13.3915 + 10.8773i 0.538684 + 0.437549i
\(619\) 14.1035 34.0488i 0.566866 1.36854i −0.337317 0.941391i \(-0.609519\pi\)
0.904183 0.427145i \(-0.140481\pi\)
\(620\) 3.38964 17.9894i 0.136131 0.722472i
\(621\) 2.51411 6.06961i 0.100888 0.243565i
\(622\) 9.16009 30.7556i 0.367286 1.23319i
\(623\) 1.06155i 0.0425299i
\(624\) 17.9450 + 10.7633i 0.718374 + 0.430878i
\(625\) 46.9479i 1.87791i
\(626\) −6.52650 1.94382i −0.260851 0.0776907i
\(627\) −0.197358 + 0.476465i −0.00788173 + 0.0190282i
\(628\) −3.46969 5.08080i −0.138456 0.202746i
\(629\) 19.5789 47.2677i 0.780663 1.88469i
\(630\) 0.540093 0.664931i 0.0215178 0.0264915i
\(631\) 17.1976i 0.684626i 0.939586 + 0.342313i \(0.111210\pi\)
−0.939586 + 0.342313i \(0.888790\pi\)
\(632\) 40.5419 + 3.37318i 1.61267 + 0.134178i
\(633\) −14.1738 + 14.1738i −0.563358 + 0.563358i
\(634\) 28.8549 + 23.4375i 1.14597 + 0.930822i
\(635\) −52.7756 21.8604i −2.09434 0.867503i
\(636\) −6.04301 3.95004i −0.239621 0.156629i
\(637\) 13.3632 21.2916i 0.529470 0.843604i
\(638\) 0.0478556 0.160678i 0.00189462 0.00636131i
\(639\) −7.87337 + 7.87337i −0.311466 + 0.311466i
\(640\) 2.87008 45.6471i 0.113450 1.80436i
\(641\) 30.1213i 1.18972i −0.803830 0.594859i \(-0.797208\pi\)
0.803830 0.594859i \(-0.202792\pi\)
\(642\) 18.4628 + 34.1254i 0.728669 + 1.34682i
\(643\) 11.6851 + 28.2104i 0.460817 + 1.11251i 0.968062 + 0.250709i \(0.0806638\pi\)
−0.507245 + 0.861802i \(0.669336\pi\)
\(644\) 0.381057 0.0798097i 0.0150157 0.00314494i
\(645\) 17.5739 42.4270i 0.691970 1.67056i
\(646\) 14.8380 + 12.0522i 0.583792 + 0.474188i
\(647\) 13.9589 13.9589i 0.548781 0.548781i −0.377307 0.926088i \(-0.623150\pi\)
0.926088 + 0.377307i \(0.123150\pi\)
\(648\) 1.29331 15.5442i 0.0508061 0.610634i
\(649\) −1.11104 + 1.11104i −0.0436123 + 0.0436123i
\(650\) 38.1739 + 43.4509i 1.49730 + 1.70428i
\(651\) 0.508187 0.210498i 0.0199174 0.00825006i
\(652\) −4.10862 + 21.8052i −0.160906 + 0.853957i
\(653\) −3.10496 1.28612i −0.121507 0.0503297i 0.321102 0.947045i \(-0.395947\pi\)
−0.442608 + 0.896715i \(0.645947\pi\)
\(654\) −4.41971 + 2.39118i −0.172824 + 0.0935026i
\(655\) −52.4870 52.4870i −2.05084 2.05084i
\(656\) 5.78795 2.53573i 0.225982 0.0990035i
\(657\) −5.65240 5.65240i −0.220521 0.220521i
\(658\) 1.65009 + 0.491456i 0.0643273 + 0.0191589i
\(659\) −8.54734 + 20.6351i −0.332957 + 0.803830i 0.665398 + 0.746489i \(0.268262\pi\)
−0.998355 + 0.0573404i \(0.981738\pi\)
\(660\) −0.271562 + 1.44123i −0.0105705 + 0.0560998i
\(661\) 4.42699 + 1.83372i 0.172190 + 0.0713234i 0.467113 0.884198i \(-0.345294\pi\)
−0.294923 + 0.955521i \(0.595294\pi\)
\(662\) 1.98214 + 19.1331i 0.0770381 + 0.743628i
\(663\) −20.2764 + 14.4025i −0.787471 + 0.559346i
\(664\) −29.8557 + 9.55333i −1.15863 + 0.370741i
\(665\) 1.92458 0.0746321
\(666\) 10.5709 + 8.58627i 0.409614 + 0.332711i
\(667\) −1.01848 + 0.421869i −0.0394358 + 0.0163348i
\(668\) −1.78781 + 2.73511i −0.0691725 + 0.105824i
\(669\) 21.7476 9.00815i 0.840811 0.348275i
\(670\) 28.7144 15.5353i 1.10933 0.600180i
\(671\) 0.323123 + 0.323123i 0.0124740 + 0.0124740i
\(672\) 1.19528 0.678268i 0.0461088 0.0261647i
\(673\) 13.4817i 0.519680i −0.965652 0.259840i \(-0.916330\pi\)
0.965652 0.259840i \(-0.0836699\pi\)
\(674\) −3.15821 5.83743i −0.121650 0.224849i
\(675\) 24.5300 59.2207i 0.944161 2.27941i
\(676\) 25.7836 + 3.34775i 0.991676 + 0.128760i
\(677\) −3.00640 + 1.24529i −0.115545 + 0.0478605i −0.439707 0.898141i \(-0.644918\pi\)
0.324162 + 0.946002i \(0.394918\pi\)
\(678\) 1.73447 0.179687i 0.0666120 0.00690084i
\(679\) 1.22211 + 1.22211i 0.0469002 + 0.0469002i
\(680\) 48.3254 + 24.8958i 1.85320 + 0.954711i
\(681\) 20.5320i 0.786787i
\(682\) 0.252380 0.310715i 0.00966412 0.0118979i
\(683\) −17.1344 + 41.3661i −0.655629 + 1.58283i 0.148858 + 0.988859i \(0.452440\pi\)
−0.804487 + 0.593970i \(0.797560\pi\)
\(684\) −4.20206 + 2.86959i −0.160670 + 0.109722i
\(685\) −42.9866 17.8056i −1.64243 0.680318i
\(686\) −1.57438 2.90998i −0.0601101 0.111104i
\(687\) 10.9169 10.9169i 0.416505 0.416505i
\(688\) −21.6923 + 22.5876i −0.827010 + 0.861146i
\(689\) −8.84430 1.49806i −0.336941 0.0570714i
\(690\) 8.48173 4.58885i 0.322894 0.174694i
\(691\) −0.00225565 0.000934320i −8.58089e−5 3.55432e-5i −0.382726 0.923862i \(-0.625015\pi\)
0.382641 + 0.923897i \(0.375015\pi\)
\(692\) 9.63477 + 14.1086i 0.366259 + 0.536328i
\(693\) 0.0173064 0.00716853i 0.000657414 0.000272310i
\(694\) 25.8003 31.7638i 0.979365 1.20574i
\(695\) 4.28408 0.162504
\(696\) −2.97035 + 2.51404i −0.112591 + 0.0952944i
\(697\) 7.51053i 0.284482i
\(698\) −12.8899 + 15.8692i −0.487889 + 0.600659i
\(699\) −15.1504 + 6.27552i −0.573042 + 0.237362i
\(700\) 3.71794 0.778697i 0.140525 0.0294320i
\(701\) −11.2131 4.64462i −0.423513 0.175425i 0.160739 0.986997i \(-0.448612\pi\)
−0.584252 + 0.811572i \(0.698612\pi\)
\(702\) −9.28659 27.2775i −0.350500 1.02952i
\(703\) 30.5965i 1.15397i
\(704\) 0.530178 0.848055i 0.0199818 0.0319623i
\(705\) 42.6468 1.60617
\(706\) −8.56579 + 28.7602i −0.322378 + 1.08240i
\(707\) −0.717984 1.73337i −0.0270026 0.0651899i
\(708\) 35.6963 7.47635i 1.34155 0.280978i
\(709\) −12.7466 + 30.7731i −0.478709 + 1.15571i 0.481505 + 0.876443i \(0.340090\pi\)
−0.960215 + 0.279263i \(0.909910\pi\)
\(710\) −70.7600 + 7.33057i −2.65558 + 0.275111i
\(711\) −9.10106 9.10106i −0.341317 0.341317i
\(712\) 1.48680 17.8697i 0.0557201 0.669695i
\(713\) −2.63215 −0.0985748
\(714\) 0.168320 + 1.62475i 0.00629923 + 0.0608048i
\(715\) 0.406398 + 1.77636i 0.0151984 + 0.0664320i
\(716\) −4.81579 + 3.28871i −0.179974 + 0.122905i
\(717\) −0.406852 0.982227i −0.0151942 0.0366819i
\(718\) −4.56624 8.43994i −0.170411 0.314976i
\(719\) 39.5495i 1.47495i 0.675376 + 0.737474i \(0.263982\pi\)
−0.675376 + 0.737474i \(0.736018\pi\)
\(720\) −10.0230 + 10.4368i −0.373537 + 0.388955i
\(721\) 0.995515 0.995515i 0.0370749 0.0370749i
\(722\) 14.7958 + 4.40672i 0.550644 + 0.164001i
\(723\) 8.15136 + 19.6791i 0.303152 + 0.731874i
\(724\) −5.68318 + 30.1617i −0.211214 + 1.12095i
\(725\) −9.93726 + 4.11615i −0.369061 + 0.152870i
\(726\) 14.2102 17.4948i 0.527392 0.649294i
\(727\) 2.37508 + 2.37508i 0.0880869 + 0.0880869i 0.749777 0.661690i \(-0.230161\pi\)
−0.661690 + 0.749777i \(0.730161\pi\)
\(728\) 1.02455 1.36608i 0.0379725 0.0506303i
\(729\) −20.8827 + 20.8827i −0.773432 + 0.773432i
\(730\) −5.26272 50.7996i −0.194782 1.88018i
\(731\) −14.2442 34.3887i −0.526843 1.27191i
\(732\) −2.17434 10.3815i −0.0803657 0.383712i
\(733\) −12.7302 + 5.27301i −0.470200 + 0.194763i −0.605186 0.796084i \(-0.706901\pi\)
0.134986 + 0.990848i \(0.456901\pi\)
\(734\) −4.84899 8.96256i −0.178979 0.330814i
\(735\) −28.9166 28.9166i −1.06660 1.06660i
\(736\) −6.52635 + 0.809781i −0.240565 + 0.0298489i
\(737\) 0.713907 0.0262971
\(738\) −1.91602 0.570660i −0.0705298 0.0210063i
\(739\) 35.0677 14.5255i 1.28998 0.534329i 0.371004 0.928631i \(-0.379014\pi\)
0.918981 + 0.394302i \(0.129014\pi\)
\(740\) 17.8365 + 85.1614i 0.655681 + 3.13059i
\(741\) 7.90678 12.5979i 0.290463 0.462794i
\(742\) −0.371439 + 0.457294i −0.0136360 + 0.0167878i
\(743\) 11.2363i 0.412219i 0.978529 + 0.206109i \(0.0660802\pi\)
−0.978529 + 0.206109i \(0.933920\pi\)
\(744\) −8.84946 + 2.83168i −0.324437 + 0.103814i
\(745\) 5.80149 5.80149i 0.212550 0.212550i
\(746\) −28.5596 + 35.1609i −1.04564 + 1.28733i
\(747\) 9.16252 + 3.79524i 0.335239 + 0.138861i
\(748\) 0.670378 + 0.981662i 0.0245114 + 0.0358931i
\(749\) 2.92521 1.21166i 0.106885 0.0442731i
\(750\) 46.2768 25.0370i 1.68979 0.914222i
\(751\) 3.24205i 0.118304i −0.998249 0.0591520i \(-0.981160\pi\)
0.998249 0.0591520i \(-0.0188396\pi\)
\(752\) −27.0887 10.5841i −0.987824 0.385962i
\(753\) 41.8095 1.52362
\(754\) −2.13468 + 4.33843i −0.0777403 + 0.157996i
\(755\) 23.4863 56.7008i 0.854752 2.06355i
\(756\) −1.85975 0.350422i −0.0676386 0.0127447i
\(757\) 9.49906 + 22.9328i 0.345249 + 0.833505i 0.997167 + 0.0752157i \(0.0239645\pi\)
−0.651918 + 0.758289i \(0.726035\pi\)
\(758\) −20.0826 + 2.08050i −0.729431 + 0.0755673i
\(759\) 0.210876 0.00765431
\(760\) −32.3977 2.69556i −1.17519 0.0977783i
\(761\) 6.33846i 0.229769i −0.993379 0.114884i \(-0.963350\pi\)
0.993379 0.114884i \(-0.0366498\pi\)
\(762\) 2.98773 + 28.8397i 0.108234 + 1.04475i
\(763\) 0.156926 + 0.378854i 0.00568111 + 0.0137154i
\(764\) −21.5704 14.0996i −0.780391 0.510105i
\(765\) −6.58164 15.8895i −0.237960 0.574485i
\(766\) −5.69054 1.69484i −0.205608 0.0612372i
\(767\) 36.9441 26.2416i 1.33397 0.947530i
\(768\) −21.0708 + 9.74362i −0.760329 + 0.351593i
\(769\) 5.25446 + 5.25446i 0.189481 + 0.189481i 0.795472 0.605991i \(-0.207223\pi\)
−0.605991 + 0.795472i \(0.707223\pi\)
\(770\) 0.114701 + 0.0341619i 0.00413352 + 0.00123111i
\(771\) 0.827533 1.99784i 0.0298029 0.0719505i
\(772\) −6.28654 30.0155i −0.226257 1.08028i
\(773\) −10.3185 4.27408i −0.371132 0.153728i 0.189319 0.981916i \(-0.439372\pi\)
−0.560451 + 0.828188i \(0.689372\pi\)
\(774\) 9.85524 1.02098i 0.354239 0.0366983i
\(775\) −25.6817 −0.922514
\(776\) −18.8609 22.2842i −0.677066 0.799957i
\(777\) −1.84869 + 1.84869i −0.0663216 + 0.0663216i
\(778\) 33.2374 40.9199i 1.19162 1.46705i
\(779\) −1.71883 4.14963i −0.0615835 0.148676i
\(780\) 14.6635 39.6738i 0.525036 1.42055i
\(781\) −1.43719 0.595302i −0.0514266 0.0213016i
\(782\) 2.23115 7.49121i 0.0797857 0.267885i
\(783\) 5.35867 0.191503
\(784\) 11.1909 + 25.5440i 0.399676 + 0.912285i
\(785\) −8.79371 + 8.79371i −0.313861 + 0.313861i
\(786\) −10.7542 + 36.1079i −0.383590 + 1.28793i
\(787\) −3.34644 8.07902i −0.119288 0.287986i 0.852946 0.522000i \(-0.174814\pi\)
−0.972233 + 0.234014i \(0.924814\pi\)
\(788\) 3.55511 2.42779i 0.126646 0.0864864i
\(789\) 16.2410 + 39.2091i 0.578193 + 1.39588i
\(790\) −8.47363 81.7936i −0.301478 2.91009i
\(791\) 0.142298i 0.00505952i
\(792\) −0.301369 + 0.0964333i −0.0107087 + 0.00342661i
\(793\) −7.63181 10.7444i −0.271014 0.381544i
\(794\) 2.40868 + 1.95646i 0.0854808 + 0.0694322i
\(795\) −5.58445 + 13.4821i −0.198060 + 0.478159i
\(796\) 1.82755 + 8.72576i 0.0647758 + 0.309276i
\(797\) −48.3650 20.0334i −1.71318 0.709621i −0.999962 0.00867511i \(-0.997239\pi\)
−0.713214 0.700946i \(-0.752761\pi\)
\(798\) −0.464832 0.859166i −0.0164549 0.0304141i
\(799\) 24.4424 24.4424i 0.864710 0.864710i
\(800\) −63.6771 + 7.90098i −2.25133 + 0.279342i
\(801\) −4.01148 + 4.01148i −0.141739 + 0.141739i
\(802\) −0.771973 + 2.59194i −0.0272593 + 0.0915247i
\(803\) 0.427375 1.03178i 0.0150818 0.0364106i
\(804\) −13.8704 9.06645i −0.489172 0.319749i
\(805\) −0.301153 0.727047i −0.0106142 0.0256250i
\(806\) −8.67301 + 7.61971i −0.305494 + 0.268393i
\(807\) 6.92468 + 6.92468i 0.243760 + 0.243760i
\(808\) 9.65854 + 30.1845i 0.339786 + 1.06189i
\(809\) −22.9976 22.9976i −0.808554 0.808554i 0.175861 0.984415i \(-0.443729\pi\)
−0.984415 + 0.175861i \(0.943729\pi\)
\(810\) −31.3606 + 3.24888i −1.10190 + 0.114154i
\(811\) −42.9227 17.7792i −1.50722 0.624311i −0.532238 0.846595i \(-0.678649\pi\)
−0.974982 + 0.222284i \(0.928649\pi\)
\(812\) 0.179086 + 0.262243i 0.00628469 + 0.00920293i
\(813\) −26.0061 + 10.7721i −0.912074 + 0.377793i
\(814\) −0.543097 + 1.82348i −0.0190356 + 0.0639130i
\(815\) 44.8509 1.57106
\(816\) −0.557825 27.5862i −0.0195278 0.965711i
\(817\) 15.7401 + 15.7401i 0.550677 + 0.550677i
\(818\) −15.6375 28.9033i −0.546751 1.01058i
\(819\) −0.526638 + 0.120485i −0.0184022 + 0.00421008i
\(820\) −7.20319 10.5479i −0.251546 0.368350i
\(821\) −12.2894 + 29.6693i −0.428903 + 1.03546i 0.550732 + 0.834682i \(0.314348\pi\)
−0.979636 + 0.200782i \(0.935652\pi\)
\(822\) 2.43355 + 23.4904i 0.0848799 + 0.819323i
\(823\) 11.8152 + 11.8152i 0.411852 + 0.411852i 0.882383 0.470531i \(-0.155938\pi\)
−0.470531 + 0.882383i \(0.655938\pi\)
\(824\) −18.1525 + 15.3638i −0.632371 + 0.535225i
\(825\) 2.05750 0.0716329
\(826\) −0.306683 2.96033i −0.0106709 0.103003i
\(827\) 27.6770 + 11.4642i 0.962424 + 0.398649i 0.807887 0.589338i \(-0.200611\pi\)
0.154537 + 0.987987i \(0.450611\pi\)
\(828\) 1.74157 + 1.13838i 0.0605237 + 0.0395616i
\(829\) −43.1698 17.8815i −1.49935 0.621050i −0.526021 0.850472i \(-0.676317\pi\)
−0.973327 + 0.229421i \(0.926317\pi\)
\(830\) 30.1508 + 55.7287i 1.04655 + 1.93437i
\(831\) −38.2360 −1.32639
\(832\) −19.1603 + 21.5611i −0.664265 + 0.747498i
\(833\) −33.1463 −1.14845
\(834\) −1.03471 1.91249i −0.0358290 0.0662240i
\(835\) 6.10207 + 2.52756i 0.211171 + 0.0874698i
\(836\) −0.595048 0.388955i −0.0205802 0.0134523i
\(837\) 11.8208 + 4.89632i 0.408585 + 0.169241i
\(838\) −0.890265 8.59349i −0.0307537 0.296857i
\(839\) 24.5761 0.848461 0.424230 0.905554i \(-0.360545\pi\)
0.424230 + 0.905554i \(0.360545\pi\)
\(840\) −1.79466 2.12040i −0.0619215 0.0731606i
\(841\) 19.8703 + 19.8703i 0.685182 + 0.685182i
\(842\) −2.51934 24.3186i −0.0868223 0.838073i
\(843\) 17.7266 42.7959i 0.610538 1.47397i
\(844\) −15.5822 22.8176i −0.536361 0.785415i
\(845\) −3.00039 52.4686i −0.103217 1.80498i
\(846\) 4.37837 + 8.09270i 0.150532 + 0.278233i
\(847\) −1.30056 1.30056i −0.0446876 0.0446876i
\(848\) 6.89316 7.17769i 0.236712 0.246483i
\(849\) 25.7926 0.885200
\(850\) 21.7692 73.0912i 0.746676 2.50701i
\(851\) 11.5584 4.78765i 0.396217 0.164119i
\(852\) 20.3627 + 29.8180i 0.697615 + 1.02155i
\(853\) 14.3436 + 5.94133i 0.491116 + 0.203427i 0.614477 0.788935i \(-0.289367\pi\)
−0.123360 + 0.992362i \(0.539367\pi\)
\(854\) −0.860948 + 0.0891922i −0.0294610 + 0.00305209i
\(855\) 7.27281 + 7.27281i 0.248725 + 0.248725i
\(856\) −50.9389 + 16.2996i −1.74106 + 0.557110i
\(857\) 11.7757 + 11.7757i 0.402251 + 0.402251i 0.879026 0.476774i \(-0.158194\pi\)
−0.476774 + 0.879026i \(0.658194\pi\)
\(858\) 0.694842 0.610456i 0.0237215 0.0208406i
\(859\) −7.95322 19.2008i −0.271360 0.655122i 0.728182 0.685384i \(-0.240366\pi\)
−0.999542 + 0.0302622i \(0.990366\pi\)
\(860\) 52.9863 + 34.6347i 1.80682 + 1.18103i
\(861\) 0.146873 0.354582i 0.00500541 0.0120841i
\(862\) −2.71007 + 9.09922i −0.0923054 + 0.309921i
\(863\) −40.6507 + 40.6507i −1.38377 + 1.38377i −0.545949 + 0.837818i \(0.683831\pi\)
−0.837818 + 0.545949i \(0.816169\pi\)
\(864\) 30.8156 + 8.50364i 1.04837 + 0.289300i
\(865\) 24.4187 24.4187i 0.830262 0.830262i
\(866\) −23.7914 43.9744i −0.808464 1.49431i
\(867\) 7.51014 + 3.11080i 0.255058 + 0.105648i
\(868\) 0.155432 + 0.742120i 0.00527570 + 0.0251892i
\(869\) 0.688128 1.66129i 0.0233431 0.0563553i
\(870\) 6.10555 + 4.95926i 0.206997 + 0.168135i
\(871\) −20.3002 3.43846i −0.687845 0.116508i
\(872\) −2.11102 6.59728i −0.0714882 0.223412i
\(873\) 9.23647i 0.312607i
\(874\) 0.481684 + 4.64956i 0.0162932 + 0.157274i
\(875\) −1.64311 3.96681i −0.0555471 0.134103i
\(876\) −21.4067 + 14.6187i −0.723266 + 0.493919i
\(877\) 11.6600 + 28.1496i 0.393729 + 0.950545i 0.989120 + 0.147109i \(0.0469969\pi\)
−0.595392 + 0.803436i \(0.703003\pi\)
\(878\) 12.0796 40.5578i 0.407665 1.36876i
\(879\) −5.92861 + 5.92861i −0.199967 + 0.199967i
\(880\) −1.88298 0.735718i −0.0634753 0.0248011i
\(881\) 5.99203 0.201877 0.100938 0.994893i \(-0.467816\pi\)
0.100938 + 0.994893i \(0.467816\pi\)
\(882\) 2.51849 8.45599i 0.0848021 0.284728i
\(883\) −40.2702 16.6805i −1.35520 0.561342i −0.417464 0.908693i \(-0.637081\pi\)
−0.937735 + 0.347351i \(0.887081\pi\)
\(884\) −14.3343 31.1426i −0.482115 1.04744i
\(885\) −28.2112 68.1077i −0.948308 2.28942i
\(886\) 16.9405 20.8562i 0.569129 0.700678i
\(887\) −25.5472 + 25.5472i −0.857791 + 0.857791i −0.991078 0.133287i \(-0.957447\pi\)
0.133287 + 0.991078i \(0.457447\pi\)
\(888\) 33.7095 28.5310i 1.13122 0.957438i
\(889\) 2.36604 0.0793543
\(890\) −36.0522 + 3.73493i −1.20847 + 0.125195i
\(891\) −0.636955 0.263836i −0.0213388 0.00883882i
\(892\) 6.65163 + 31.7586i 0.222713 + 1.06336i
\(893\) −7.91082 + 19.0984i −0.264725 + 0.639104i
\(894\) −3.99108 1.18869i −0.133482 0.0397556i
\(895\) 8.33503 + 8.33503i 0.278609 + 0.278609i
\(896\) 0.613702 + 1.79225i 0.0205024 + 0.0598748i
\(897\) −5.99631 1.01566i −0.200211 0.0339119i
\(898\) 20.2770 + 6.03921i 0.676652 + 0.201531i
\(899\) −0.821603 1.98353i −0.0274020 0.0661543i
\(900\) 16.9924 + 11.1071i 0.566412 + 0.370238i
\(901\) 4.52640 + 10.9277i 0.150796 + 0.364054i
\(902\) −0.0287813 0.277818i −0.000958311 0.00925032i
\(903\) 1.90209i 0.0632976i
\(904\) −0.199301 + 2.39539i −0.00662867 + 0.0796694i
\(905\) 62.0393 2.06225
\(906\) −30.9847 + 3.20994i −1.02940 + 0.106643i
\(907\) −3.10397 7.49364i −0.103066 0.248822i 0.863932 0.503609i \(-0.167995\pi\)
−0.966997 + 0.254787i \(0.917995\pi\)
\(908\) −27.8127 5.24058i −0.922997 0.173915i
\(909\) 3.83703 9.26342i 0.127266 0.307248i
\(910\) −3.09701 1.52385i −0.102665 0.0505150i
\(911\) −52.0385 −1.72411 −0.862056 0.506814i \(-0.830823\pi\)
−0.862056 + 0.506814i \(0.830823\pi\)
\(912\) 6.62148 + 15.1139i 0.219259 + 0.500472i
\(913\) 1.38555i 0.0458549i
\(914\) −10.5398 + 5.70231i −0.348625 + 0.188616i
\(915\) −19.8077 + 8.20461i −0.654822 + 0.271236i
\(916\) 12.0016 + 17.5745i 0.396545 + 0.580677i
\(917\) 2.84044 + 1.17655i 0.0937996 + 0.0388530i
\(918\) −23.9550 + 29.4920i −0.790633 + 0.973381i
\(919\) −6.59859 + 6.59859i −0.217667 + 0.217667i −0.807515 0.589847i \(-0.799188\pi\)
0.589847 + 0.807515i \(0.299188\pi\)
\(920\) 4.05120 + 12.6606i 0.133564 + 0.417409i
\(921\) 34.4306i 1.13453i
\(922\) 18.9836 23.3715i 0.625191 0.769698i
\(923\) 37.9996 + 23.8496i 1.25077 + 0.785020i
\(924\) −0.0124525 0.0594552i −0.000409656 0.00195593i
\(925\) 112.775 46.7128i 3.70801 1.53591i
\(926\) −35.2898 10.5106i −1.15970 0.345398i
\(927\) 7.52392 0.247118
\(928\) −2.64738 4.66534i −0.0869044 0.153147i
\(929\) 21.4042 + 21.4042i 0.702248 + 0.702248i 0.964893 0.262644i \(-0.0845946\pi\)
−0.262644 + 0.964893i \(0.584595\pi\)
\(930\) 8.93693 + 16.5184i 0.293053 + 0.541661i
\(931\) 18.3136 7.58572i 0.600202 0.248612i
\(932\) −4.63385 22.1246i −0.151787 0.724716i
\(933\) 12.5993 + 30.4173i 0.412481 + 0.995818i
\(934\) 5.33721 + 51.5187i 0.174639 + 1.68574i
\(935\) 1.69903 1.69903i 0.0555643 0.0555643i
\(936\) 9.03398 1.29059i 0.295285 0.0421844i
\(937\) −12.8168 12.8168i −0.418706 0.418706i 0.466052 0.884758i \(-0.345676\pi\)
−0.884758 + 0.466052i \(0.845676\pi\)
\(938\) −0.852557 + 1.04962i −0.0278370 + 0.0342712i
\(939\) 6.45472 2.67363i 0.210642 0.0872507i
\(940\) −10.8852 + 57.7696i −0.355035 + 1.88424i
\(941\) −20.6559 49.8677i −0.673362 1.62564i −0.775859 0.630907i \(-0.782683\pi\)
0.102496 0.994733i \(-0.467317\pi\)
\(942\) 6.04955 + 1.80177i 0.197105 + 0.0587049i
\(943\) −1.29864 + 1.29864i −0.0422896 + 0.0422896i
\(944\) 1.01637 + 50.2627i 0.0330800 + 1.63591i
\(945\) 3.82531i 0.124437i
\(946\) 0.658682 + 1.21747i 0.0214156 + 0.0395832i
\(947\) −10.1294 24.4546i −0.329162 0.794666i −0.998655 0.0518483i \(-0.983489\pi\)
0.669493 0.742818i \(-0.266511\pi\)
\(948\) −34.4675 + 23.5379i −1.11945 + 0.764475i
\(949\) −17.1220 + 27.2804i −0.555803 + 0.885560i
\(950\) 4.69975 + 45.3655i 0.152480 + 1.47185i
\(951\) −38.1389 −1.23674
\(952\) −2.24386 0.186694i −0.0727238 0.00605078i
\(953\) 6.86834 + 6.86834i 0.222487 + 0.222487i 0.809545 0.587058i \(-0.199714\pi\)
−0.587058 + 0.809545i \(0.699714\pi\)
\(954\) −3.13170 + 0.324437i −0.101393 + 0.0105040i
\(955\) −19.9336 + 48.1240i −0.645036 + 1.55725i
\(956\) 1.43437 0.300420i 0.0463910 0.00971627i
\(957\) 0.0658231 + 0.158911i 0.00212776 + 0.00513686i
\(958\) 4.99367 16.7666i 0.161338 0.541703i
\(959\) 1.92718 0.0622317
\(960\) 27.2408 + 38.2076i 0.879193 + 1.23314i
\(961\) 25.8738i 0.834639i
\(962\) 24.2257 49.2354i 0.781069 1.58741i
\(963\) 15.6328 + 6.47533i 0.503761 + 0.208665i
\(964\) −28.7380 + 6.01897i −0.925588 + 0.193858i
\(965\) −57.2689 + 23.7215i −1.84355 + 0.763623i
\(966\) −0.251831 + 0.310039i −0.00810252 + 0.00997534i
\(967\) 39.4567i 1.26884i −0.772987 0.634422i \(-0.781238\pi\)
0.772987 0.634422i \(-0.218762\pi\)
\(968\) 20.0715 + 23.7146i 0.645124 + 0.762218i
\(969\) −19.6121 −0.630030
\(970\) −37.2054 + 45.8051i −1.19459 + 1.47071i
\(971\) −17.5788 + 7.28136i −0.564129 + 0.233670i −0.646477 0.762934i \(-0.723758\pi\)
0.0823474 + 0.996604i \(0.473758\pi\)
\(972\) −10.0968 14.7852i −0.323856 0.474235i
\(973\) −0.163937 + 0.0679049i −0.00525557 + 0.00217693i
\(974\) 31.1011 16.8265i 0.996542 0.539157i
\(975\) −58.5056 9.90973i −1.87368 0.317365i
\(976\) 14.6178 0.295589i 0.467905 0.00946157i
\(977\) 23.0721 23.0721i 0.738142 0.738142i −0.234076 0.972218i \(-0.575207\pi\)
0.972218 + 0.234076i \(0.0752065\pi\)
\(978\) −10.8326 20.0222i −0.346387 0.640239i
\(979\) −0.732246 0.303306i −0.0234027 0.00969371i
\(980\) 46.5512 31.7899i 1.48702 1.01549i
\(981\) −0.838642 + 2.02466i −0.0267758 + 0.0646425i
\(982\) 19.6568 24.2003i 0.627274 0.772263i
\(983\) 18.0009i 0.574140i 0.957910 + 0.287070i \(0.0926813\pi\)
−0.957910 + 0.287070i \(0.907319\pi\)
\(984\) −2.96903 + 5.76320i −0.0946493 + 0.183724i
\(985\) −6.15308 6.15308i −0.196054 0.196054i
\(986\) 6.34164 0.656978i 0.201959 0.0209225i
\(987\) −1.63194 + 0.675973i −0.0519454 + 0.0215165i
\(988\) 15.0470 + 13.9260i 0.478709 + 0.443046i
\(989\) 3.48316 8.40909i 0.110758 0.267394i
\(990\) 0.304348 + 0.562537i 0.00967282 + 0.0178786i
\(991\) 43.1924i 1.37205i −0.727577 0.686026i \(-0.759354\pi\)
0.727577 0.686026i \(-0.240646\pi\)
\(992\) −1.57707 12.7103i −0.0500722 0.403552i
\(993\) −13.9545 13.9545i −0.442833 0.442833i
\(994\) 2.59155 1.40210i 0.0821988 0.0444718i
\(995\) 16.6486 6.89606i 0.527795 0.218620i
\(996\) 17.5961 26.9196i 0.557554 0.852981i
\(997\) −29.6069 + 12.2636i −0.937660 + 0.388392i −0.798579 0.601889i \(-0.794415\pi\)
−0.139081 + 0.990281i \(0.544415\pi\)
\(998\) 9.19037 + 7.46493i 0.290916 + 0.236298i
\(999\) −60.8138 −1.92406
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 416.2.bi.a.307.19 yes 216
13.5 odd 4 416.2.bd.a.83.10 216
32.27 odd 8 416.2.bd.a.411.10 yes 216
416.187 even 8 inner 416.2.bi.a.187.19 yes 216
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
416.2.bd.a.83.10 216 13.5 odd 4
416.2.bd.a.411.10 yes 216 32.27 odd 8
416.2.bi.a.187.19 yes 216 416.187 even 8 inner
416.2.bi.a.307.19 yes 216 1.1 even 1 trivial